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Multiple Target Tracking with RF Sensor Networks

Maurizio Bocca, Ossi Kaltiokallio, Neal Patwari, Suresh Venkatasubramanian

arXiv:1302.4720v1cs.NI

TL;DR

The paper addresses real-time device-free tracking of multiple people when trajectories intersect and target counts change. It combines multi-channel RSS radio tomographic imaging with machine-vision tracking adaptations, demonstrating real-time tracking of up to four targets in three indoor environments. The system correctly estimates target counts and reports tracking RMSE from 0.27 m to 0.52 m across tested conditions.

  • Problem

    Prior RF-sensor-network research mainly focused on single targets, while practical systems must track multiple targets in real time through intersecting trajectories and changing target counts.

  • Method

    The system forms RTI images from multi-channel RSS using fade-level weighting and adapts machine-vision methods to detect and track target blobs.

  • Results

    The system accurately tracked up to four intersecting targets in real time across open, apartment, and cluttered office environments, with tracking RMSE from 0.27 m to 0.52 m.

  • Takeaways & Limitations

    The results support real-time device-free tracking of multiple targets in cluttered indoor environments while correctly estimating how many targets are present.

  • Takeaways & Limitations

    When targets converge and then separate, the system has a high probability of losing the correct track-to-blob association.

Abstract

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RF sensor networks are wireless networks that can localize and track people (or targets) without needing them to carry or wear any electronic device. They use the change in the received signal strength (RSS) of the links due to the movements of people to infer their locations. In this paper, we consider real-time multiple target tracking with RF sensor networks. We perform radio tomographic imaging (RTI), which generates images of the change in the propagation field, as if they were frames of a video. Our RTI method uses RSS measurements on multiple frequency channels on each link, combining them with a fade level-based weighted average. We describe methods to adapt machine vision methods to the peculiarities of RTI to enable real time multiple target tracking. Several tests are performed in an open environment, a one-bedroom apartment, and a cluttered office environment. The results demonstrate that the system is capable of accurately tracking in real-time up to 4 targets in cluttered indoor environments, even when their trajectories intersect multiple times, without mis-estimating the number of targets found in the monitored area. The highest average tracking error measured in the tests is 0.45 m with two targets, 0.46 m with three targets, and 0.55 m with four targets.

I. INTRODUCTION

RF sensor networks enable device-free localization from RSS changes, but prior work largely addressed single targets. This paper targets real-time tracking of multiple people in indoor environments, including intersecting trajectories and changing target counts.

  • I. INTRODUCTION: RF sensor networks localize and track people from RSS changes without requiring them to carry radio devices.RSS measurements can form radio tomographic images of propagation-field changes caused by people and objects.
  • I. INTRODUCTION: Multiple-target tracking must handle intersecting trajectories, target entry and exit, and correct estimation of the number of targets.Noise and simultaneous targets can create spurious, disappearing, merging, or splitting blobs in RTI images.
  • I. INTRODUCTION: Prior RSS-based multi-target methods were non-real-time, limited in target count, assumed a known target number, or avoided intersecting trajectories.The paper evaluates three settings: an open environment, a one-bedroom apartment, and a heavily cluttered office.
  • I. INTRODUCTION: Multipath fading makes RSS responses depend on frequency and device position in obstructed environments.The paper estimates fade levels across channels to distinguish deep-fade and anti-fade links during measurement processing.

B. Measurement model

The measurement model converts multi-channel RSS changes into a linear estimate of the monitored propagation field. It uses fade-level weighting, an ellipse-based link model, and regularized least squares for real-time reconstruction.

  • B. Measurement model: RSS changes are weighted by channel fade level because anti-fade channels provide more informative localization measurements.For each link, the weighted RSS change is computed from the difference between current and reference RSS.
  • B. Measurement model: The discretized propagation field models each link’s RSS change as a linear combination of voxel contributions plus link noise.Each voxel has a link-specific weight indicating how strongly it affects that link.
  • B. Measurement model: The ellipse model assigns nonzero voxel weights inside the ellipse whose foci are the transmitter and receiver, and zero weights outside it.Within the ellipse, the weight is constant and inversely proportional to the ellipse area.
  • B. Measurement model: Across all links, the model estimates the propagation-field change vector from weighted RSS measurements using a regularized least-squares inverse.Regularization is required because recovering the image from link measurements is ill-posed.
  • B. Measurement model: The real-time image estimate uses a linear transformation computed once before operation and requires MN operations.The paper states that this computation can be performed in real time.

D. Image denoising

RTI images are denoised with isotropic Gaussian filtering to suppress small spurious blobs while preserving target-sized regions. The filtered image is computed by neighborhood-weighted convolution.

  • D. Image denoising: RTI images can contain small spurious blobs because of RSS noise, multiple people, and obstructions.These artifacts do not correspond to actual targets and motivate image denoising before tracking.
  • D. Image denoising: The denoising step convolves the RTI image with an isotropic Gaussian kernel.Each filtered voxel becomes a weighted average of its neighborhood, with central pixels receiving greater weight.
  • D. Image denoising: σG = 1 m controls the Gaussian blur, while rG = 0.75 m sets the kernel radius.The kernel parameters are chosen to fit the size of blobs corresponding to targets.

III. MULTIPLE TARGET TRACKING

The tracking pipeline treats RTI images as video frames and adaptively filters them before clustering. Its thresholding preserves target regions while reducing the voxels passed to clustering.

  • III. MULTIPLE TARGET TRACKING: RTI images are processed as video-like frames to detect target blobs and track multiple targets in real time.The tracking objective includes detecting target entrance and exit from the monitored area.
  • III. MULTIPLE TARGET TRACKING: A dynamic threshold reduces the voxel set passed to clustering while preserving regions occupied by targets.The threshold is based on calibration intensity when no targets are present and target intensities during tracking.
  • III. MULTIPLE TARGET TRACKING: During tracking, the minimum target intensity is low-pass filtered before updating the threshold.The filter uses αf = 0.9.
  • III. MULTIPLE TARGET TRACKING: The online threshold update keeps voxels surrounding existing tracks from being filtered out.The experiments found no significant performance change for β values from 0.75 to 0.9.
  • III. MULTIPLE TARGET TRACKING: A binary mask retains voxels whose denoised intensity exceeds the threshold, and the filtered image is the element-wise product of the denoised image and mask.The retained voxels are then used to form the set processed by clustering.

B. Clustering

The clustering phase groups thresholded RTI voxels into blobs without assuming the number of targets, then represents each cluster by its highest-intensity voxel.

  • HAC starts with each unfiltered voxel as an independent cluster and repeatedly merges the two closest clusters.Unfiltered voxels are those whose filtered-image intensity exceeds the threshold Tt.
  • The average linkage distance between voxel clusters is the mean Euclidean distance across voxels assigned to the two clusters.
  • Clustering stops when the minimum intercluster distance exceeds Tc, with lower Tc producing more smaller clusters and higher Tc fewer larger clusters.
  • Voxel intensities are normalized to the range [0, 1] before cluster representatives are selected.
  • For each cluster, the voxel with maximum normalized intensity becomes its cluster head, forming the original head set H.

C. Cluster heads selection

Cluster-head selection reduces redundant representatives while retaining strong responses near tracked targets and all heads in entrance or exit regions.

  • The method selects a higher-intensity subset HI from the original cluster heads H to reduce association complexity while retaining representatives for occupied regions.
  • All cluster heads within the entrance/exit voxel set Re are retained regardless of intensity.Re may cover a specific entrance area or the monitored perimeter, depending on the environment.
  • For remaining heads, gating retains candidates near previously tracked target positions and subsequent intensity thresholding filters weak heads.
  • Each gating radius accommodates target motion variance and RTI noise, including spurious, disappearing, merging, and splitting blobs.The radius is enlarged when a target trajectory intersects another track.
  • Selected heads update existing tracks, while unassigned heads in Re can initiate candidate tracks and those outside Re are discarded as noise.Tracks are deleted after no assigned head appears for ndel consecutive frames, limiting deletion caused by short-term image noise.

2) Target tracking:

Target tracking is formulated as frame-by-frame assignment of RTI observations to existing tracks, using nearest-neighbor methods adapted for real-time operation and changing target counts.

  • At each RTI frame, selected cluster heads HI are assigned to estimated targets T through a data assignment problem.The assignment seeks an optimal permutation represented by a permutation matrix Θ.
  • The association matrix Ω marks infeasible observation-target pairs with ∞, turning assignment into total-cost minimization.
  • Prior PDA and JPDA methods assume a known constant target count, while PF and MHT face real-time or computational limitations.MHT hypothesis growth is exponential in the number of targets and postpones assignment until later information is available.
  • The paper tailors global and greedy nearest-neighbor methods to RTI, updating tracks at every frame with one-to-one track-observation associations.
  • GNN uses the Hungarian algorithm to find an optimal assignment in polynomial time O(n^3), whereas SNN uses a faster O(n) greedy selection without optimality guarantees.Here n = min(|T|, |HI|).

E. Kalman filter tracking

The tracker initializes parallel track-specific Kalman filters for confirmed targets and updates each filter from its prior state and associated observation. The experiments use specified reconstruction, tracking, hardware, and deployment settings across indoor environments.

  • E. Kalman filter tracking: Each confirmed candidate track initializes a track-specific Kalman filter that recursively estimates its position from the previous state and associated cluster head.The filters run in parallel under Brownian-motion and Gaussian-measurement-noise assumptions.
  • E. Kalman filter tracking: The experiments specify image-reconstruction and multiple-target-tracking parameters in Tables I and II.
  • E. Kalman filter tracking: The sensor nodes use multi-channel token passing, with packets carrying each transmitter’s ID and the latest RSS measurements received from other sensors.The nodes transmit in TDMA fashion based on their ID number.
  • E. Kalman filter tracking: The nodes operate in the 2.4 GHz ISM band across 16 selectable channels spaced 5 MHz apart, with carrier frequency fc = 2405 + 5 · (c −11) MHz.
  • E. Kalman filter tracking: Tests span an open environment with no obstructions, a furnished one-bedroom apartment, and an office with interference from multiple 802.11 b/g networks.

1) Open environment:

The open-environment tests examine two people following predefined paths, including a case where their trajectories intersect. The section also introduces the tracking evaluation measures and the office-test processing-time comparison.

  • 1) Open environment:: In the open environment, two people walk at constant speed along a predefined rectangular path, entering sequentially in the same or opposite directions.The opposite-direction test makes their trajectories intersect and then diverge at the same monitored point.
  • 1) Open environment:: The apartment deployment uses 33 sensors over 58m2, while the office deployment uses 32 sensors over 67m2 with two, three, and four people walking simultaneously.
  • 1) Open environment:: Table III compares processing times for the GNN, SNN, and MHT multiple-target tracking methods.
  • 1) Open environment:: The cardinality error is the fraction of test frames in which the true and estimated numbers of people differ.
  • 1) Open environment:: The OMAT error is the RMSE of the best possible association between estimated and real targets, using q = 2.

3) OSPA metric:

OSPA augments target-position comparison with a cardinality penalty, while Q95 evaluates consistency during intersecting trajectories. Results and figures report target-count tracking and trajectory accuracy in office tests.

  • 3) OSPA metric:: OSPA adds a constant g, measured in meters, to penalize cardinality error alongside position discrepancies.
  • 3) OSPA metric:: Q95 is the 95%-percentile of OMAT errors and indicates whether tracks remain consistent during and after intersecting trajectories.
  • 3) OSPA metric:: The cardinality error is limited to a few frames before target entrance and after target exit, as shown in the office tests.The passage attributes this behavior to the confirmation and deletion rules.
  • 3) OSPA metric:: Multiple frequency channels can sometimes compensate for confirmation-rule delays in detecting target entrance.Deep-fade links may produce RSS variation before a person reaches the link line, allowing successive confirmations to anticipate entrance.
  • 3) OSPA metric:: With intersecting office trajectories, one test reports ϵO = 0.44 m and Q95 = 0.99 m despite multiple intersections.

3) Tracking accuracy and consistency:

The system maintains accurate and consistent multi-target tracking across increasingly challenging environments, including intersecting trajectories and cluttered office settings. GNN performance becomes more advantageous as RTI images become noisier, while target-count estimation remains robust.

  • Tracking accuracy: 0.55 m is the largest average OMAT error, measured with four intersecting targets in the multipath-dominated office environment.The corresponding largest open-environment OMAT errors are 0.33 m and 0.30 m.
  • Tracking accuracy: Approximately 0.30 m average OMAT error is measured in both apartment tests with the GNN and SNN methods.Differences in ϵO and Q95 between the tests arise from how separated the two people’s paths are.
  • Tracking accuracy: 0.55 m and 1.26 m are the largest ϵO and Q95 values for four intersecting targets in the cluttered office environment.For separated trajectories, the corresponding values are 0.45 m and 0.96 m.
  • Tracking consistency: The GNN method yields more consistent Q95 improvement as images become noisier, especially when four targets with intersecting trajectories are tracked.GNN finds the optimal data-association solution at each frame.
  • Target-count consistency: Average OSPA errors increase only slightly at g = 5 because frames with mismatched estimated and observed target cardinalities are rare.This holds despite making no assumption about the number of targets in the monitored area.

4) Sensitivity analysis:

The paper evaluates sensitivity and practical applicability across environments and tracking conditions. It reports real-time tracking for up to four intersecting targets, while identifying difficult association cases for future work.

  • Sensitivity analysis: 0.54 m to 0.74 m is the range of ϵO values across clustering thresholds Tc in the four-target intersecting-trajectory office test.Tc controls average cluster size and ultimately the number of clusters.
  • Sensitivity analysis: Tracking accuracy remains consistent across different Tc values, but small thresholds prevent real-time RTI-image processing.The passage links Tc to cluster formation and processing behavior.
  • Experimental scope: The experiments cover an open environment, a furnished apartment, and a heavily cluttered office environment.Up to four targets with intersecting trajectories are tracked across these settings.
  • Experimental results: 0.27 m to 0.52 m is the measured tracking RMSE range, from two intersecting targets in the apartment to four in the office.The reported range spans the tested environments and target counts.
  • Experimental results: The system correctly estimates the number of targets and tracks them in real time across all three environments, including intersecting trajectories.The tests do not assume that the target count is known a priori.
  • Limitations: The system has a high probability of losing correct track-to-blob associations when targets converge and then separate again.The authors propose active badges and the AGAPE method as future remedies.
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